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Math Problems
Algebra 2
Simplify radical expressions with root inside the root
c=\frac{ab}{a+b} \text{ Isolate } a
\newline
A) a = (bc)/(b-c)
\newline
B) a = (bc)/(c-b)
\newline
C) a = (bc)/(c+b)
\newline
D) a = (bc)/(b+c)
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\qquad \left(n^
6
6
6
k^{
14
14
14
}\right)^
5
5
5
Which of the following is equivalent to the given expression?
\newline
A) n^{
30
30
30
}k^{
70
70
70
}
\newline
B) n^{
11
11
11
}k^{
19
19
19
}
\newline
C) n^{
30
30
30
}k^{
19
19
19
}
\newline
D) n^{
11
11
11
}k^{
70
70
70
}
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Which sign makes the statement true?
\newline
2.10
2.10
2.10
?
\text{?}
?
3.7
3.7
3.7
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which sign makes the statement true?
\newline
21
2
\frac{21}{2}
2
21
?
\text{?}
?
0
0
0
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which sign makes the statement true?
\newline
3.5
?
3
3.5 \, ? \, 3
3.5
?
3
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which sign makes the statement true?
\newline
0
?
−
3.75
0 \,?\, -3.75
0
?
−
3.75
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which sign makes the statement true?
\newline
0.5
0.5
0.5
?
\text{?}
?
1
2
\frac{1}{2}
2
1
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which sign makes the statement true?
\newline
−
41
2
?
−
4
-\frac{41}{2} \,?\, -4
−
2
41
?
−
4
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which sign makes the statement true?
\newline
−
41
2
?
0
-\frac{41}{2} \,?\, 0
−
2
41
?
0
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Is this an expression or an equation?
\newline
42
−
(
6
×
2
)
42 - (6 \times 2)
42
−
(
6
×
2
)
\newline
Choices:
\newline
(A)expression
\newline
(B)equation
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Which sign makes the statement true?
\newline
−
4
5
?
5.2
-\frac{4}{5} \,?\, 5.2
−
5
4
?
5.2
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which sign makes the statement true?
\newline
6
?
6
1
2
6 \,?\, 6\frac{1}{2}
6
?
6
2
1
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which of the following expressions is equivalent to
−
3
(
x
2
−
4
y
2
)
-3\left(x^{2}-4 y^{2}\right)
−
3
(
x
2
−
4
y
2
)
?
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Which of the following is equivalent to
−
8
x
2
−
8
x
y
+
12
y
2
-8 x^{2}-8 x y+12 y^{2}
−
8
x
2
−
8
x
y
+
12
y
2
?
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Which sign makes the statement true?
\newline
0.5
?
50
%
0.5 \, ? \, 50\%
0.5
?
50%
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which expression is equivalent to
7
w
+
7
w
7w + 7w
7
w
+
7
w
?
\newline
Choices:
\newline
(A)
14
w
14w
14
w
\newline
(B)
w
14
w^{14}
w
14
\newline
(C)
13
w
13w
13
w
\newline
(D)
w
+
14
w + 14
w
+
14
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Solve for
m
m
m
. Express your answer in simplest radical form if necessary.
\newline
m
3
=
125
m^{3}=125
m
3
=
125
\newline
Answer:
m
=
m=
m
=
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Solve for
a
a
a
. Express your answer in simplest radical form if necessary.
\newline
a
=
(
30.7
)
2
a=(\sqrt{30.7})^{2}
a
=
(
30.7
)
2
\newline
Answer:
a
=
a=
a
=
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Solve for
a
a
a
. Express your answer in simplest radical form if necessary.
\newline
a
=
(
61
)
2
a=(\sqrt{61})^{2}
a
=
(
61
)
2
\newline
Answer:
a
=
a=
a
=
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Use the Mean Value Theorem to establish the following inequality for
x
>
0
x>0
x
>
0
:
\newline
1
<
e
x
−
1
ln
(
x
+
1
)
<
(
x
+
1
)
e
x
1<\frac{e^{x}-1}{\ln (x+1)}<(x+1) e^{x}
1
<
ln
(
x
+
1
)
e
x
−
1
<
(
x
+
1
)
e
x
\newline
Deduce the following limit :
\newline
lim
x
→
0
e
x
−
1
ln
(
x
+
1
)
\lim _{x \rightarrow 0} \frac{e^{x}-1}{\ln (x+1)}
x
→
0
lim
ln
(
x
+
1
)
e
x
−
1
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Which expression is equivalent to
9
y
+
5
y
9y + 5y
9
y
+
5
y
?
\newline
Choices:
\newline
(A)
15
y
15y
15
y
\newline
(B)
y
+
14
y + 14
y
+
14
\newline
(C)
y
14
y^{14}
y
14
\newline
(D)
14
y
14y
14
y
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Which expression is equivalent to
2
y
+
6
y
2y + 6y
2
y
+
6
y
?
\newline
Choices:
\newline
(A)
y
+
8
y + 8
y
+
8
\newline
(B)
8
y
8y
8
y
\newline
(C)
y
8
y^8
y
8
\newline
(D)
9
y
9y
9
y
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Which expression is equivalent to the expression below?
\newline
4
(
5
h
)
+
6
h
4(5 h)+6 h
4
(
5
h
)
+
6
h
\newline
44
h
44 h
44
h
\newline
20
h
+
5
h
2
20 h+5 h^{2}
20
h
+
5
h
2
\newline
11
h
+
4
11 h+4
11
h
+
4
\newline
26
h
26 h
26
h
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Which expression is equivalent to the expression below?
\newline
p
+
p
+
p
+
p
p+p+p+p
p
+
p
+
p
+
p
\newline
4
p
4 p
4
p
\newline
4
4
4
\newline
p
4
\frac{p}{4}
4
p
\newline
p
4
p^{4}
p
4
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Which of the following is a rational number?
\newline
Choices:
\newline
(A)
5
\sqrt{5}
5
\newline
(B)
π
\pi
π
\newline
(C)
6
\sqrt{6}
6
\newline
(D)
6.333
…
6.333\ldots
6.333
…
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Which of the following is an integer?
\newline
Choices:
\newline
(A)
6
\sqrt{6}
6
\newline
(B)
π
\pi
π
\newline
(C)
2
\sqrt{2}
2
\newline
(D)
6
6
6
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Simplify.
\newline
Rewrite the expression in the form
x
n
x^{n}
x
n
.
\newline
x
6
x
8
=
□
\frac{x^{6}}{x^{8}}=\square
x
8
x
6
=
□
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Identify the following as either an expression or an equation.
\newline
10
x
2
+
4
x
−
3
10x^{2}+4x-3
10
x
2
+
4
x
−
3
\newline
A) expression
\newline
B) equation
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Fully simplify.
\newline
(
6
x
5
y
2
)
3
\left(6 x^{5} y^{2}\right)^{3}
(
6
x
5
y
2
)
3
\newline
Answer:
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Express in simplest radical form.
\newline
560
7
\frac{\sqrt{560}}{\sqrt{7}}
7
560
\newline
Answer:
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Given
x
>
0
x>0
x
>
0
, the expression
x
19
\sqrt{x^{19}}
x
19
is equivalent to
\newline
x
8
x
2
x^{8} \sqrt{x^{2}}
x
8
x
2
\newline
x
8
x
x^{8} \sqrt{x}
x
8
x
\newline
x
9
x
x^{9} \sqrt{x}
x
9
x
\newline
x
9
x
2
x^{9} \sqrt{x^{2}}
x
9
x
2
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
7
x
3
y
2
45
x
5
y
4
7 x^{3} y^{2} \sqrt{45 x^{5} y^{4}}
7
x
3
y
2
45
x
5
y
4
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
y
3
24
x
5
y
2
y^{3} \sqrt{24 x^{5} y^{2}}
y
3
24
x
5
y
2
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
2
27
x
3
y
4
2 \sqrt{27 x^{3} y^{4}}
2
27
x
3
y
4
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
8
x
2
252
x
2
y
4
8 x^{2} \sqrt{252 x^{2} y^{4}}
8
x
2
252
x
2
y
4
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
x
2
y
2
24
x
4
y
2
x^{2} y^{2} \sqrt{24 x^{4} y^{2}}
x
2
y
2
24
x
4
y
2
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
7
y
3
36
x
6
y
5
7 y^{3} \sqrt{36 x^{6} y^{5}}
7
y
3
36
x
6
y
5
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
3
x
2
y
2
28
x
5
y
2
3 x^{2} y^{2} \sqrt{28 x^{5} y^{2}}
3
x
2
y
2
28
x
5
y
2
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
4
x
2
y
3
27
x
2
y
7
4 x^{2} y^{3} \sqrt{27 x^{2} y^{7}}
4
x
2
y
3
27
x
2
y
7
\newline
Answer:
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Select the expression that is equivalent to
1
3
x
−
1
2
\frac{1}{3 x^{-\frac{1}{2}}}
3
x
−
2
1
1
\newline
3
x
2
\sqrt{3 x^{2}}
3
x
2
\newline
x
2
3
\frac{\sqrt{x^{2}}}{3}
3
x
2
\newline
x
3
\frac{\sqrt{x}}{3}
3
x
\newline
3
x
\sqrt{3 x}
3
x
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Select the expression that is equivalent to
2
x
−
1
2
2 x^{-\frac{1}{2}}
2
x
−
2
1
\newline
2
x
2
\frac{2}{\sqrt{x^{2}}}
x
2
2
\newline
1
2
x
2
\frac{1}{\sqrt{2 x^{2}}}
2
x
2
1
\newline
1
2
x
\frac{1}{\sqrt{2 x}}
2
x
1
\newline
2
x
\frac{2}{\sqrt{x}}
x
2
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Fully simplify using only positive exponents.
\newline
2
x
8
y
6
4
x
5
y
5
\frac{2 x^{8} y^{6}}{4 x^{5} y^{5}}
4
x
5
y
5
2
x
8
y
6
\newline
Answer:
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d
d
x
=
−
(
x
+
1
)
2
\frac{d}{d x}=-(x+1)^{2}
d
x
d
=
−
(
x
+
1
)
2
Get tutor help
Fully simplify using only positive exponents.
\newline
8
x
8
y
8
8
x
6
y
5
\frac{8 x^{8} y^{8}}{8 x^{6} y^{5}}
8
x
6
y
5
8
x
8
y
8
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
9
x
5
y
3
9
x
2
y
\frac{9 x^{5} y^{3}}{9 x^{2} y}
9
x
2
y
9
x
5
y
3
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
125
x
3
y
2
x
5
y
3
\frac{125 x^{3} y^{2}}{x^{5} y^{3}}
x
5
y
3
125
x
3
y
2
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
5
x
4
y
2
125
x
3
y
4
\frac{5 x^{4} y^{2}}{125 x^{3} y^{4}}
125
x
3
y
4
5
x
4
y
2
\newline
Answer:
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Which expression is equivalent to
(
3
2
×
3
−
1
)
2
\left(3^{2} \times 3^{-1}\right)^{2}
(
3
2
×
3
−
1
)
2
?
\newline
9
9
9
\newline
1
9
\frac{1}{9}
9
1
\newline
81
81
81
\newline
27
27
27
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Find
d
d
p
(
4
p
4
−
4
sin
p
)
\frac{d}{d p}\left(4 p^{4}-4 \sin p\right)
d
p
d
(
4
p
4
−
4
sin
p
)
\newline
Answer:
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Find
d
d
x
(
4
cos
2
x
)
\frac{d}{d x}(4 \cos 2 x)
d
x
d
(
4
cos
2
x
)
\newline
Answer:
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